REVIEW OF SCIENTIFIC INSTRUMENTS 84, 056101 (2013)
Note: Magnetic noise from the inner wall of a magnetically shielded room
Sheraz Khan1,2 and David Cohen2,3,4,a)
1
Department of Neurology, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts
02129, USA
2
A. A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital/Massachusetts Institute of
Technology/Harvard University, Boston, Massachusetts 02129, USA
3
Department of Radiology, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts
02129, USA
4
Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts
02139, USA
(Received 27 February 2013; accepted 6 April 2013; published online 1 May 2013)
We measured the thermal magnetic noise generated by the inner high-permeability wall of a magnetically shielded room. This room houses a magnetoencephalogram (MEG), which contains 102 “small”
identical magnetometers. For the measurement, we created two large magnetometers by summing the
outputs of 46 magnetometers equally on the helmet’s left and right side, to look at the summed noise
of the right and left vertical walls. From these summed outputs,
we calculated the rms noise amplitude
√
due to all six walls at the MEG location to be ∼0.5 f T/ Hz at 100 Hz, only slowly rising with lower
frequency. This is well below the system noise of each small MEG magnetometer, hence is negligible
for the MEG. © 2013 Author(s). All article content, except where otherwise noted, is licensed under
a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4802845]
The magnetically shielded room (MSR) plays an important role in the technology of brain imaging; every magnetoencephalogram (MEG) detection system1, 2 is now enclosed
inside an MSR,3 where the purpose is to exclude external
magnetic fluctuating disturbances from the sensitive MEG detectors. The MSR is generally made up of alternate layers of
metal with high permeability, such as moly-permalloy, and
metal with high conductivity, usually aluminum. The high
permeability layers shield equally against any frequency of
external disturbance, as the induced poles counter the external field. In the high conductivity layers, eddy currents are
induced which oppose the fluctuating external field, the effect
rising with frequency. But the inner wall, nearly always chosen to be the high permeability metal, can itself be a source
of magnetic noise4 because of thermally generated electronic
current (Johnson-noise) and magnetic domain motion (related to “magnetic viscosity”). If these two thermal noises are
large enough, they could interfere with MEG measurements,
hence it is important to know their magnitude. Although several groups have estimated this noise theoretically,5–8 and
performed measurements of noise from small simple shield
geometries,6, 7 there have been no direct measurements from
the inner wall of an actual, full-size room. We here present
such direct data.
An actual, direct measurement is necessary because the
theoretical estimates for small, simple geometries when extrapolated to a full-size room can lead to considerable error. These estimates were performed by two groups. First,
a Helsinki (Finland) group calculated the magnetic noise
from simple high-permeability metal shapes due to Johnson
noise,5, 6 but did not include the thermal domain noise, hence
a) Author to whom correspondence should be addressed. Electronic mail:
davcohen@mit.edu
0034-6748/2013/84(5)/056101/3/$30.00
the estimates may have been too low. They also performed
noise measurements from simple shapes of high-permeability
metal,6 but in their case the extrapolation to a large room is
mathematically very cumbersome. Second, a Princeton (U.S.)
group calculated the noise from simple high- permeability
shapes and included domain noise,7 but the extrapolation to
a large room is again difficult. However, they also measured
the noise in a small ferrite shield,8 which indeed allowed
√ some
extrapolation to a large room. This yielded ∼0.7 f T/ Hz as
the three-dimensional noise amplitude at low frequencies, say
>10 Hz; but Johnson noise was neglected here. Concerning
the frequency (f) dependence, the various theoretical calculations show a variety of complex dependencies, almost all in
1
the range of f 0 to f − 2 , that is, they all show only a slow rise
with decreasing frequency.7 All in all, a direct noise measurement would therefore be valuable.
We performed the measurement by using most of the 102
magnetometers in our MEG system, a VectorView made by
Elekta Neuromag Oy. These magnetometers are oriented approximately parallel to the scalp thereby sensing the component of magnetic field approximately normal to the scalp.
From these “small” magnetometers, we created two extrasensitive large-area magnetometers by summing the output
amplitudes of 46 identical magnetometers equally on the right
(r) and left (l) sides of the MEG helmet, with r and l as seen
from an imaginary MEG subject’s point of view. The output was a weighted amplitude sum of 46 small magnetometers on each side. That is, we have twice “tied together” 46
small magnetometers to make two large magnetometers, with
higher signal/noise ratio (S/N) than each of the small ones.
This was necessary because the estimates suggest the wall
noise should be well below the system noise of each MEG
small magnetometer, hence would not be directly measurable
with these small units.
84, 056101-1
© Author(s) 2013
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
66.55.152.53 On: Thu, 22 Oct 2015 02:36:46
056101-2
S. Khan and D. Cohen
FIG. 1. Looking down on the inner layer of the MSR, with inside dimensions of 3.0 m (in x), 4.0 m (in y), and 2.4 m (in z). This layer consists of
four sheets of 1 mm moly-permalloy, mounted on a high-conductivity aluminum layer of 10 mm thickness. The MSR contains the MEG helmet with
102 magnetometers (small squares), of which 46 on each side are summed
separately, to make two large magnetometers. These measure the magnetic
noise in the x-direction, generated thermally in the left and right walls. The
nose of an imagined MEG subject is seen at the left of the helmet. The inset
is a perspective view of the same helmet.
The setup is shown in Fig. 1, where the purpose is to measure the magnetic noise in the x-direction due to the two vertical y-z walls, right and left. We used open-source MEG processing software Brainstorm9 to compute these geometrical
properties of the magnetometers. We assign different weights
to each small magnetometer, equal to the cosine of its angle to the x-axis, as implied in Fig. 2. The effective area of
each large magnetometer is thus calculated to be 28 times the
small area, or 56 times when both are summed
or subtracted,
√
hence increasing the S/N by a factor of 56 = 7.5. We have,
here, assumed uncorrelated noise in each small magnetometer. However, it is known that some of the MEG system noise
is due to the Johnson noise in the r-f shield of the dewar,10
which would correlate some of the noise in neighboring small
magnetometers; the net effect would be to increase the system noise of each large magnetometer, hence somewhat re-
FIG. 2. Each magnetometer is assigned a weight from 0 to 1, depending on
its angle to the x-direction. Taking all weights into account, the total effective
area on each side is 28 times the area of each small square. Extreme left-right
magnetometers have a weight of 1.0 and they are about 22 cm apart, resulting
in incomplete cancellation of wall noise due to its x-gradient.
Rev. Sci. Instrum. 84, 056101 (2013)
duce the factor of 7.5 for both, as we shall see. It should also
be noted, by examining the inset of Fig. 1, that the x-signals in
the large magnetometers will be contaminated by some y and
z magnetic noise signal. For example z-noise will couple with
small magnetometers that are tilted both in the x and z directions. However, this contamination is calculated to be negligible due to the relatively small y and z magnetometers areas.
These areas are relatively 3.1/56 and 7.2/56, respectively, and
assuming the y and z-noise is the same as x-noise, to first order. That is, assuming the x, y, and z-noise are uncorrelated
and add in quadrature, the quadratic sum of x-noise + y-noise
+z-noise is <1% greater than the x-noise by itself; hence this
contamination can be neglected.
In measuring the x-noise, our basic idea here is to use the
two large magnetometers in both the l + r summing mode and
in the l − r subtraction mode, and then subtract the latter from
the former output. This leaves approximately twice the total
wall noise, because it has been included twice, one from each
large magnetometer. Stated otherwise, in the summing mode,
the grand output is equal to the summed internal noise plus
twice the noise of both right and left walls. In the subtraction
mode, the grand output is again due to the summed internal
noise, but the wall noise will be largely cancelled because the
left and right magnetometers are quite close together in the xdirection, although not completely so, because wall noise will
have some gradient in the x-direction. The summed minus the
subtracted mode then approximately yields twice the total xnoise, which is what we first seek.
The measured data is shown in Fig. 3, in the form of a
frequency analysis. The data were recorded at 04 AM when
mechanical wall vibrations are least. It is seen, nevertheless,
that there are large magnetic artifacts due to vibrations, which
render the curves <50 Hz to be mostly unusable here. Large
artifacts are also produced by 60 Hz and its harmonics. Both
these types of artifacts are present in almost all MSRs and can
only be reduced with great difficulty. However, there are also
seen to be two frequency regions, which are almost clear of
artifacts and readily usable for our purposes. In one of these
regions we arbitrarily choose 100 Hz as our main frequency
of interest.
In extracting numbers, we first look at the upper, 1curve, due to a single small magnetometer.
We see, at
√
100 Hz, a mean noise of 2.6 f T/ Hz, in agreement with
Elekta’s commercial specifications. We compare this to the
3-curve (summed noise of only 92
√ small magnetometers),
with a value at 100 Hz of 0.51 f T/ Hz, resulting in a sensitivity improvement of 2.6/0.51 = 5.1. This is not the ideal factor of 7.5 we would have liked, where the degradation is here
due to the correlated thermal-shield noise, as mentioned earlier. However, a noise reduction of 5.1 is adequate enough to
allow our wall measurement. Next, we note that the summed
value (2-curve in Fig. 3) is 0.78. The total x-direction wall
noise, added in twice, is then the difference between these
two values, in quadrature, i.e.,
(2 x total wall noise)2 = (0.78)2 − (0.51)2 ,
from which we calculate that the total x-noise of both√l and r
walls, at the location of the MEG helmet, is 0.30 f T/ Hz.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
66.55.152.53 On: Thu, 22 Oct 2015 02:36:46
056101-3
S. Khan and D. Cohen
FIG. 3. Frequency analysis of a wall-noise measurement, for 30 min recording. The MEG bandwidth was 0.1 to 200 Hz, the sampling rate was 600 Hz, at
24 bits. Three sets of data are shown: (1) A single channel chosen which directly faces x-ward. (2) The two large magnetometers, added together. (3) The
same but in the subtracted mode. Only two “clear” sections of the 1-curve are
shown, to avoid crowding. The complete lower two curves are dominated by
usual MSR artifacts: wall vibrations below 50 Hz, and 60 Hz and its harmonics. However, two regions are indicated which are almost clear of artifacts,
hence due only to broad-band noise. Two vibration peaks are labeled “a”
and “b.”
We have, here, assumed that, in the subtracted value (3curve), the wall noises cancel out exactly, but we know this
cannot be true because of their x-gradients; however we justify this assumption as follows. We note that the vibration
artifacts have a range of cancellation, because of variation
in their gradients. For example, peak “a” at 12 Hz is only
2/3 cancelled, while peak “b” at 42 Hz is almost completely
cancelled. Let us assume, conservatively about halfway, that
the wall noise
is 85–90% cancelled, leaving an uncancelled
√
0.03 f T/ Hz. However, 0.03 added in quadrature to 0.51
makes only a negligible difference,
√ and can here be ignored,
therefore we retain our 0.30 f T/ Hz as the total wall noise
in the x-direction, at 100 Hz.
Next, we try to extract wall-noise data at frequencies
other than 100 Hz. Looking at higher frequencies in Fig. 3,
we see no significant change in the difference between 2 and
3 curves for frequencies up to 165 Hz, as high as we go
here. Going back lower than 100 Hz, we stop at, say, 80 Hz.
The 2-curve is slightly elevated here, but this could well be
a spillover from 60 Hz, hence we draw no conclusion. Going lower, we can first guess the shape of the 1-curve, if it
were free of vibration artifact. At frequencies below about
10 Hz, it shows the rapid rise of the characteristic f −1 curve of
these magnetometers, but before that, there are two frequencies which are almost artifact-free: 16 Hz and 10 Hz. There
are 2-curve uncertainties, but using our previous
√ logic, we
calculate: at 16 Hz, total√x-noise = ∼0.36 f T/ Hz and at
10 Hz it is = ∼0.41 f T/ Hz, as only very approximate values. However there is clearly no rapid rise with lower frequencies, in agreement with the theoretical estimates (Table I
of Ref. 7). That is, while curves 2 and 3 each show a rapid rise
with decreasing frequency, the difference between these two
curves does not rise in this way. In fact, the curves can be seen
to cross at 4 Hz, which is an acceptable statistical fluctuation
involving both curves.
Further, we can expand the x-noise value of 0.30, which
is only one component of the wall-noise vector, to obtain the
Rev. Sci. Instrum. 84, 056101 (2013)
amplitude of the three-dimensional wall-noise vector, at the
location of the MEG helmet in the MSR. This is the quantity
finally needed, to be of general use, and allows comparison
with the similar value extrapolated from the previously mentioned ferrite shield.8 To do this, although the wall distances
to the helmet are, here, different in y and z in comparison to x,
we are, here, justified in assuming
√ they are the same, allow√
ing us to simply multiply 0.3 by 3, obtaining ∼0.5 f T/ Hz
as the three-dimensional rms noise amplitude. We are justified because we are, here, only interested in first-order accuracy; the smaller z-spacing (than x-spacing) will give a larger
z-value than 0.3, but the situation is reversed for y-spacing,
partially canceling the z-value error, keeping our errors reasonably small.
In comparison with the extrapolated value of
√
8
∼0.7 f T/ Hz from the small
√ ferrite shield measurement, our
final value of ∼0.5 f T/ Hz is somewhat less, especially so
when the ferrite value should be the low side because it ignores thermal currents. But our value, based on an actual MSR
measurement, should perhaps be more valid because there are
fewer uncertainties.
Finally, we point out that the noise measured here is specific to our particular MSR. Although most MSR’s in use today have about the same internal dimensions, but the number
of 1 mm sheets can vary from one to four, i.e., the inner-wall
thickness can vary from 1 to 4 mm. The thicker this highpermeability wall, the better it will shield the Johnson noise
from the aluminum layer on which it is mounted, this noise
could be comparatively large, depending upon the aluminumlayer conductivity. We expect the 4 mm wall to almost completely block out the aluminum Johnson noise, while a 1 mm
wall would allow a large fraction to get through to the magnetometers.
Therefore, all-in-all, thermal magnetic noise from the inner high-permeability wall of an MSR is negligible, in comparison with internal systematic noise for present-day MEG
usage, especially if the inner wall is at least 3 mm thick. We
conclude that this MEG systematic noise can be much reduced before thermal wall noise becomes a limiting factor.
The Authors thank Seppo Ahlfors, Santosh Ganesan,
Martin Luessi, Dimitrios Pantazis, and Matti Hamalainen for
their help.
1 D.
Cohen, Science 175, 664 (1972).
Salmelin and S. Baillet, Hum. Brain Mapp 30, 1753 (2009).
3 D. Cohen, U. Schlapfer, S. Ahlfors, M. Hamalainen, and E. Halgren, in
Biomag 96: Proceedings of the 13th International Conference on Biomagnetism, edited by H. Nowak, J. Haueisen, F. Giessler, and R. Huonker
(VDE, Berlin, 1997), p. 399.
4 J. A. Sidles, J. L. Garbini, W. M. Dougherty, and Shih-hui Chao, Proc.
IEEE 91(5), 799 (2003).
5 J. Nenonen and T. Katila, in: Biomag 87: Proceedings of the 6th International Conference on Biomagnetism, edited by K. Atsumi, M. Kotani,
S. Ueno, T. Katila, and S. J. Williamson (Denki University Press, Tokyo,
1988), p. 426.
6 J. Nenonen, J. Montonen, and T. Katila, Rev. Sci. Instrum. 67, 2397 (1996).
7 T. W. Kornack, S. J. Smullin, S-K. Lee, and M. V. Romalis, Appl. Phys.
Lett. 90, 223501 (2007).
8 S. K. Lee and M. V. Romalis, J. Appl. Phys. 103, 084904 (2008).
9 F. Tadel, S. Baillet, J. C. Mosher, D. Pantazis, and R. M. Leahy, Comput.
Intell. Neurosci. 2011, 879716 (2011).
10 M. Hamalainen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V.
Lounasmaa, Rev. Mod. Phys. 65, 413 (1993).
2 R.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:
66.55.152.53 On: Thu, 22 Oct 2015 02:36:46